Group #31907376 — subgroups

Subgroups — #31907376

Order 18176.

364 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22597053	C₂	1	1	yes	maximal, characteristic
2	#22590143	C₂	1	1	yes	maximal, characteristic, complemented
3	#22586296	C₂	1	4	yes	maximal, complemented
4	C₇₁×#2162	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#14556134	—	2	1	no	—
6	#17986549	C₄	1	1	yes	characteristic
7	#17986078	—	2	1	no	—
8	#17986078	C₄	1	2	yes	—
9	C₈×D₂₈₄	—	2	1	no	—
10	C₈×D₂₈₄	C₂²	1	2	yes	—
11	#17986023	C₄	1	1	yes	characteristic
12	#17985965	—	2	1	no	—
13	C₄⋊(C₇₁⋊C₁₆)	C₂²	1	2	yes	—
14	C₂²⋊(C₇₁⋊C₁₆)	—	2	1	no	—
15	#17985775	—	2	1	no	—
16	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
17	C₄⋊C₁₆×C₇₁	—	2	1	no	—
18	C₂²⋊C₁₆×C₇₁	—	2	1	no	—
19	C₄×C₁₆×C₇₁	C₂²	1	2	yes	—
20	C₂×#11765865	—	2	1	no	—
21	#14556134	—	4	4	no	—
22	C₂×#11765849	—	2	1	no	—
23	C₂×#11765848	—	2	2	no	—
24	C₂×C₈×D₇₁	—	2	2	no	—
25	#14556128	C₈	1	1	yes	characteristic
26	#14556125	C₈	1	1	yes	characteristic
27	#14556116	—	2	1	no	—
28	#14556102	—	2	1	no	—
29	#14556102	C₈	1	2	yes	—
30	C₄×D₂₈₄	—	2	1	no	—
31	C₄×D₂₈₄	C₂×C₄	1	2	yes	—
32	C₂×C₇₁⋊C₁₆	—	2	2	no	—
33	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
34	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	2	yes	—
35	(C₂×D₇₁)⋊C₈	—	2	2	no	—
36	(C₂×D₇₁)⋊C₈	—	2	2	no	—
37	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
40	C₂×C₁₆×C₇₁	—	2	2	no	—
41	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
42	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
43	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
44	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
45	#11765865	—	4	2	no	—
46	#11765865	—	4	2	no	—
47	C₂×Dic₁₄₂	—	2	1	no	—
48	C₂×D₂₈₄	—	2	1	no	—
49	C₂×D₂₈₄	—	2	1	no	—
50	C₂×D₂₈₄	C₂×C₈	1	2	yes	—
51	C₂×C₂²⋊D₇₁	—	2	2	no	—
52	C₂×C₄×D₇₁	—	2	2	no	—
53	#11765849	—	4	2	no	—
54	#11765848	—	4	4	no	—
55	C₂×C₇₁⋊C₈	—	2	2	no	—
56	C₈×D₇₁	—	4	4	no	—
57	C₄⋊Dic₇₁	—	2	1	no	—
58	C₄⋊Dic₇₁	C₂×C₈	1	2	yes	—
59	(C₂×D₇₁)⋊C₄	—	2	2	no	—
60	(C₂×D₇₁)⋊C₄	—	2	2	no	—
61	C₇₁⋊C₁₆	—	4	2	no	—
62	C₂²×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
64	C₂²×C₄×C₇₁	M₁₆	1	1	yes	characteristic
65	C₂×C₈×C₇₁	—	2	2	no	—
66	C₂×C₈×C₇₁	—	4	1	no	—
67	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
70	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
72	C₄²×C₇₁	C₂×C₈	1	1	yes	characteristic
73	C₄²×C₇₁	M₁₆	1	1	yes	characteristic
74	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
75	C₁₆×C₇₁	—	4	2	no	—
76	C₂³×C₇₁	C₂²⋊C₈	1	1	yes	characteristic
77	C₂²×D₇₁	—	2	2	no	—
78	C₂×C₄×C₇₁	—	2	1	no	—
79	C₂×C₄×C₇₁	—	2	1	no	—
80	C₂×C₄×C₇₁	—	2	2	no	—
81	C₂×C₄×C₇₁	—	4	1	no	—
82	C₂×C₄×C₇₁	C₂²⋊C₈	1	1	yes	characteristic
83	C₂×C₄×C₇₁	C₂²⋊C₈	1	1	yes	characteristic
84	C₂×C₄×C₇₁	C₂²⋊C₈	1	1	yes	characteristic
85	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
87	C₂×C₄×C₇₁	C₂×M₁₆	1	1	yes	characteristic
88	C₂²⋊D₇₁	—	4	4	no	—
89	C₂×Dic₇₁	—	2	2	no	—
90	D₂₈₄	—	2	4	no	—
91	D₂₈₄	—	4	2	no	—
92	D₂₈₄	—	4	2	no	—
93	C₄×D₇₁	—	4	2	no	—
94	C₄×D₇₁	—	4	2	no	—
95	Dic₁₄₂	—	4	2	no	—
96	C₈×C₇₁	—	2	1	no	—
97	C₈×C₇₁	—	2	1	no	—
98	C₈×C₇₁	—	2	1	no	—
99	C₈×C₇₁	AGL(1,ℤ/8)	1	2	yes	—
100	C₇₁⋊C₈	—	4	2	no	—
101	C₂²×C₇₁	—	2	1	no	—
102	C₂²×C₇₁	—	2	1	no	—
103	C₂²×C₇₁	—	2	1	no	—
104	C₂²×C₇₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
105	C₂×D₇₁	—	4	2	no	—
106	C₂×D₇₁	—	4	2	no	—
107	C₂×D₇₁	—	4	2	no	—
108	C₄×C₇₁	—	2	1	no	—
109	C₄×C₇₁	—	2	1	no	—
110	C₄×C₇₁	—	2	1	no	—
111	C₄×C₇₁	—	2	1	no	—
112	C₄×C₇₁	#418	1	1	yes	characteristic
113	C₄×C₇₁	#421	1	1	yes	characteristic
114	C₄×C₇₁	#504	1	2	yes	—
115	Dic₇₁	—	4	2	no	—
116	#11632	—	71	1	no	maximal, Sylow
117	C₂×C₇₁	—	4	1	no	—
118	C₂×C₇₁	#1478	1	1	yes	characteristic
119	C₂×C₇₁	#2113	1	1	yes	characteristic
120	C₂×C₇₁	#2117	1	1	yes	characteristic
121	D₇₁	—	8	2	no	—
122	#2931	—	71	1	no	—
123	#2163	—	71	1	no	—
124	#2162	D₇₁	1	1	yes	characteristic, complemented
125	D₄⋊C₁₆	—	71	4	no	—
126	C₇₁	#11632	1	1	yes	characteristic, complemented, Sylow
127	C₂×#131	—	142	1	no	—
128	#532	—	71	1	no	—
129	#436	—	71	2	no	—
130	#436	—	142	1	no	—
131	C₈×D₄	—	71	2	no	—
132	C₈×D₄	—	142	1	no	—
133	#423	—	71	1	no	—
134	#408	—	142	1	no	—
135	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
136	C₄⋊C₁₆	—	2	1	no	—
137	C₄⋊C₁₆	—	71	2	no	—
138	C₂²⋊C₁₆	—	2	1	no	—
139	C₂²⋊C₁₆	—	142	1	no	—
140	#346	—	142	1	no	—
141	C₄×C₁₆	C₂×D₇₁	1	2	yes	—
142	C₂×#41	—	142	1	no	—
143	#131	—	284	4	no	—
144	C₂×M₁₆	—	142	1	no	—
145	C₂×M₁₆	—	142	2	no	—
146	C₂²×C₈	—	142	2	no	—
147	C₂²×C₈	D₂₈₄	1	1	yes	characteristic
148	C₂²×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
149	C₄⋊Q₈	—	71	1	no	—
150	#127	—	71	1	no	—
151	#124	—	142	1	no	—
152	#121	—	71	2	no	—
153	#121	—	142	1	no	—
154	C₄×D₄	—	71	2	no	—
155	C₄×D₄	—	142	1	no	—
156	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
157	C₂×C₁₆	—	2	2	no	—
158	C₂×C₁₆	—	142	2	no	—
159	C₄⋊C₈	—	71	2	no	—
160	C₄⋊C₈	—	142	1	no	—
161	C₂²⋊C₈	—	142	2	no	—
162	C₂²⋊C₈	—	142	2	no	—
163	C₄×C₈	C₄×D₇₁	1	1	yes	characteristic
164	C₄×C₈	D₂₈₄	1	1	yes	characteristic
165	C₄×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
166	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
167	#41	—	284	2	no	—
168	#41	—	284	2	no	—
169	C₂×Q₈	—	142	1	no	—
170	C₂×D₄	—	71	2	no	—
171	C₂×D₄	—	142	2	no	—
172	C₂×D₄	—	142	1	no	—
173	C₂×D₄	—	142	1	no	—
174	C₂²×C₄	—	142	2	no	—
175	C₂²×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
176	C₂²×C₄	C₈×D₇₁	1	1	yes	characteristic
177	C₂²×C₄	#11765848	1	1	yes	characteristic
178	M₁₆	—	284	4	no	—
179	M₁₆	—	284	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	4	1	no	—
182	C₂×C₈	—	284	4	no	—
183	C₂×C₈	—	142	2	no	—
184	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
185	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
186	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
187	C₂×C₈	C₂×D₂₈₄	1	1	yes	characteristic
188	C₄⋊C₄	—	71	2	no	—
189	C₄⋊C₄	—	142	1	no	—
190	C₂²⋊C₄	—	142	2	no	—
191	C₂²⋊C₄	—	142	2	no	—
192	C₄²	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
193	C₄²	C₈×D₇₁	1	1	yes	characteristic
194	C₄²	#11765848	1	1	yes	characteristic
195	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
196	C₁₆	—	4	2	no	—
197	C₁₆	—	284	2	no	—
198	C₂³	—	142	2	no	—
199	C₂³	(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
200	Q₈	—	284	2	no	—
201	D₄	—	284	2	no	—
202	D₄	—	284	2	no	—
203	D₄	—	284	4	no	—
204	D₄	—	142	4	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	1	no	—
207	C₂×C₄	—	2	1	no	—
208	C₂×C₄	—	4	1	no	—
209	C₂×C₄	—	284	2	no	—
210	C₂×C₄	—	284	2	no	—
211	C₂×C₄	—	142	2	no	—
212	C₂×C₄	(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
213	C₂×C₄	(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
214	C₂×C₄	(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
215	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
216	C₂×C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
217	C₂×C₄	C₂×#11765848	1	1	yes	characteristic
218	C₈	—	2	1	no	—
219	C₈	—	2	1	no	—
220	C₈	—	2	1	no	—
221	C₈	—	284	2	no	—
222	C₈	#14556156	1	2	yes	—
223	C₂²	—	2	1	no	—
224	C₂²	—	2	1	no	—
225	C₂²	—	2	1	no	—
226	C₂²	—	284	2	no	—
227	C₂²	—	284	2	no	—
228	C₂²	—	284	2	no	—
229	C₂²	C₂×(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	2	1	no	—
234	C₄	—	284	2	no	—
235	C₄	#17986005	1	1	yes	characteristic
236	C₄	#17986017	1	1	yes	characteristic
237	C₄	#17986415	1	2	yes	—
238	C₂	—	4	1	no	—
239	C₂	—	568	2	no	—
240	C₂	#22586732	1	1	yes	characteristic
241	C₂	#22589953	1	1	yes	characteristic
242	C₂	#22589967	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22597053

C₂

yes

maximal, characteristic

#22590143

C₂

yes

maximal, characteristic, complemented

#22586296

C₂

yes

maximal, complemented

C₇₁×#2162

C₂

yes

maximal, characteristic, complemented

C₂×#14556134

—

#17986549

C₄

yes

characteristic

#17986078

—

#17986078

C₄

yes

—

C₈×D₂₈₄

—

C₈×D₂₈₄

C₂²

yes

—

#17986023

C₄

yes

characteristic

#17985965

—

C₄⋊(C₇₁⋊C₁₆)

C₂²

yes

—

C₂²⋊(C₇₁⋊C₁₆)

—

#17985775

—

C₂×C₄×C₈×C₇₁

C₂²

yes

characteristic

C₄⋊C₁₆×C₇₁

—

C₂²⋊C₁₆×C₇₁

—

C₄×C₁₆×C₇₁

C₂²

yes

—

—

—

—

—

C₂×C₈×D₇₁

—

#14556128

C₈

yes

characteristic

#14556125

C₈

yes

—

—

C₈

yes

—

C₄×D₂₈₄

—

C₄×D₂₈₄

C₂×C₄

yes

—

C₂×C₇₁⋊C₁₆

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

C₂×C₄

yes

—

(C₂×D₇₁)⋊C₈

—

(C₂×D₇₁)⋊C₈

—

C₂²×C₈×C₇₁

D₄

yes

characteristic

C₂²×C₈×C₇₁

D₄

yes

characteristic

C₂×C₄²×C₇₁

C₂×C₄

yes

characteristic

C₂×C₁₆×C₇₁

—

C₄×C₈×C₇₁

C₂×C₄

yes

characteristic

C₄×C₈×C₇₁

D₄

yes

characteristic

C₄×C₈×C₇₁

D₄

yes

characteristic

C₄×C₈×C₇₁

C₂³

yes

characteristic

#11765865

—

#11765865

—

C₂×Dic₁₄₂

—

C₂×D₂₈₄

—

C₂×D₂₈₄

—

C₂×D₂₈₄

C₂×C₈

yes

—

C₂×C₂²⋊D₇₁

—

C₂×C₄×D₇₁

—

#11765849

—

#11765848

—

C₂×C₇₁⋊C₈

—

C₈×D₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

C₂×C₈

yes

—

(C₂×D₇₁)⋊C₄

—

(C₂×D₇₁)⋊C₄

—

C₇₁⋊C₁₆

—

C₂²×C₄×C₇₁

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₇₁

C₂×C₈

yes

characteristic

C₂²×C₄×C₇₁

M₁₆

yes

characteristic

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₁

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₁

C₂×D₄

yes

characteristic

C₂×C₈×C₇₁

C₂×D₄

yes

characteristic

C₄²×C₇₁

C₂²⋊C₄

yes

characteristic

C₄²×C₇₁

C₂×C₈

yes

characteristic

C₄²×C₇₁

M₁₆

yes

characteristic

C₄²×C₇₁

C₂²×C₄

yes

characteristic

C₁₆×C₇₁

—

C₂³×C₇₁

C₂²⋊C₈

yes

characteristic

C₂²×D₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₇₁

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₇₁

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₇₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₁

C₂²×C₈

yes

characteristic

C₂×C₄×C₇₁

C₂×M₁₆

yes

characteristic

C₂²⋊D₇₁

—

C₂×Dic₇₁

—

D₂₈₄

—

D₂₈₄

—

D₂₈₄

—

C₄×D₇₁

—

C₄×D₇₁

—

Dic₁₄₂

—

C₈×C₇₁

—

C₈×C₇₁

—

C₈×C₇₁

—

C₈×C₇₁

AGL(1,ℤ/8)

yes

—

100

C₇₁⋊C₈

—

101

C₂²×C₇₁

—

102

C₂²×C₇₁

—

103

C₂²×C₇₁

—

104

C₂²×C₇₁

C₂×C₂²⋊C₈

yes

characteristic

105

C₂×D₇₁

—

106

C₂×D₇₁

—

107

C₂×D₇₁

—

108

C₄×C₇₁

—

109

C₄×C₇₁

—

110

C₄×C₇₁

—

111

C₄×C₇₁

—

112

C₄×C₇₁

#418

yes

characteristic

113

C₄×C₇₁

#421

yes

characteristic

114

C₄×C₇₁

#504

yes

—

115

Dic₇₁

—

116

#11632

—

maximal, Sylow

117

C₂×C₇₁

—

118

C₂×C₇₁

#1478

yes

characteristic

119

C₂×C₇₁

#2113

yes

characteristic

120

C₂×C₇₁

#2117

yes

characteristic

121

D₇₁

—

122

#2931

—

123

#2163

—

124

#2162

D₇₁

yes

characteristic, complemented

125

D₄⋊C₁₆

—

126

C₇₁

#11632

yes

characteristic, complemented, Sylow

127

C₂×#131

—

142

—

128

#532

—

129

#436

—

130

#436

—

142

—

131

C₈×D₄

—

132

C₈×D₄

—

142

—

133

#423

—

134

#408

—

142

—

135

C₂×C₄×C₈

C₂×D₇₁

yes

characteristic

136

C₄⋊C₁₆

—

137

C₄⋊C₁₆

—

138

C₂²⋊C₁₆

—

139

C₂²⋊C₁₆

—

142

—

140

#346

—

142

—

141

C₄×C₁₆

C₂×D₇₁

yes

—

142

C₂×#41

—

142

—

143

#131

—

284

—

144

C₂×M₁₆

—

142

—

145

C₂×M₁₆

—

142

—

146

C₂²×C₈

—

142

—

147

C₂²×C₈

D₂₈₄

yes

characteristic

148

C₂²×C₈

C₂²⋊D₇₁

yes

characteristic

149

C₄⋊Q₈

—

150

#127

—

151

#124

—

142

—

152

#121

—

153

#121

—

142

—

154

C₄×D₄

—

155

C₄×D₄

—

142

—

156

C₂×C₄²

C₄×D₇₁

yes

characteristic

157

C₂×C₁₆

—

158

C₂×C₁₆

—

142

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

142

—

161

C₂²⋊C₈

—

142

—

162

C₂²⋊C₈

—

142

—

163

C₄×C₈

C₄×D₇₁

yes

characteristic

164

C₄×C₈

D₂₈₄

yes

characteristic

165

C₄×C₈

C₂²⋊D₇₁

yes

characteristic

166

C₄×C₈

C₂²×D₇₁

yes

characteristic

167

#41

—

284

—

168

#41

—

284

—

169

C₂×Q₈

—

142

—

170

C₂×D₄

—

171

C₂×D₄

—

142

—

172

C₂×D₄

—

142

—

173

C₂×D₄

—

142

—

174

C₂²×C₄

—

142

—

175

C₂²×C₄

(C₂×D₇₁)⋊C₄

yes

characteristic

176

C₂²×C₄

C₈×D₇₁

yes

characteristic

177

C₂²×C₄

#11765848

yes

characteristic

178

M₁₆

—

284

—

179

M₁₆

—

284

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

284

—

183

C₂×C₈

—

142

—

184

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

185

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

186

C₂×C₈

C₂×C₂²⋊D₇₁

yes

characteristic

187

C₂×C₈

C₂×D₂₈₄

yes

characteristic

188

C₄⋊C₄

—

189

C₄⋊C₄

—

142

—

190

C₂²⋊C₄

—

142

—

191

C₂²⋊C₄

—

142

—

192

C₄²

(C₂×D₇₁)⋊C₄

yes

characteristic

193

C₄²

C₈×D₇₁

yes

characteristic

194

C₄²

#11765848

yes

characteristic

195

C₄²

C₂×C₄×D₇₁

yes

characteristic

196

C₁₆

—

197

C₁₆

—

284

—

198

C₂³

—

142

—

199

C₂³

(C₂×D₇₁)⋊C₈

yes

characteristic

200

Q₈

—

284

—

201

D₄

—

284

—

202

D₄

—

284

—

203

D₄

—

284

—

204

D₄

—

142

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

284

—

210

C₂×C₄

—

284

—

211

C₂×C₄

—

142

—

212

C₂×C₄

(C₂×D₇₁)⋊C₈

yes

characteristic

213

C₂×C₄

(C₂×D₇₁)⋊C₈

yes

characteristic

214

C₂×C₄

(C₂×D₇₁)⋊C₈

yes

characteristic

215

C₂×C₄

C₂×(C₂×D₇₁)⋊C₄

yes

characteristic

216

C₂×C₄

C₂×C₈×D₇₁

yes

characteristic

217

C₂×C₄

C₂×#11765848

yes

characteristic

218

C₈

—

219

C₈

—

220

C₈

—

221

C₈

—

284

—

222

C₈

#14556156

yes

—

223

C₂²

—

224

C₂²

—

225

C₂²

—

226

C₂²

—

284

—

227

C₂²

—

284

—

228

C₂²

—

284

—

229

C₂²

C₂×(C₂×D₇₁)⋊C₈

yes

characteristic

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

284

—

235

C₄

#17986005

yes

characteristic

236

C₄

#17986017

yes

characteristic

237

C₄

#17986415

yes

—

238

C₂

—

239

C₂

—

568

—

240

C₂

#22586732

yes

characteristic

241

C₂

#22589953

yes

characteristic

242

C₂

#22589967

yes

characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₂₈₄
commutator	C₂×C₄×C₇₁	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₇₁
Fitting	C₇₁×#2162	C₂
socle	C₂²×C₇₁	C₂×C₂²⋊C₈
prime radical	#17986549	C₄
cosocle	C₄×C₈×C₇₁	C₂³
hypercenter	#2162	D₇₁
hypocenter	C₇₁	#11632
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2162

subgroup

G/H

center

C₂×C₈

C₂×D₂₈₄

commutator

C₂×C₄×C₇₁

C₂²×C₈

Frattini

C₄×C₈

C₂²×D₇₁

Fitting

C₇₁×#2162

C₂

socle

C₂²×C₇₁

C₂×C₂²⋊C₈

prime radical

#17986549

C₄

cosocle

C₄×C₈×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2162

N	H ≅ G/N	type
2. #22590143	C₂	semidirect
3. #22586296	C₂	semidirect
4. C₇₁×#2162	C₂	semidirect
124. #2162	D₇₁	semidirect
126. C₇₁	#11632	semidirect

H ≅ G/N

type

2. #22590143

C₂

semidirect

3. #22586296

C₂

semidirect

4. C₇₁×#2162

C₂

semidirect

124. #2162

D₇₁

semidirect

126. C₇₁

#11632

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#22597053	2
#22590143	2
#22586296	2
C₇₁×#2162	2
#11632	71

subgroup

index

C₇₁×#2162

Subgroups — #31907376

Conjugacy classes of subgroups

Complements

Maximal subgroups